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Alternative Measures of Urban Form in U.S. Metropolitan Areas. Stephen Malpezzi Wen-Kai Guo University of Wisconsin-Madison. What is sprawl?. Most writers and activists fail to define sprawl. Some elements of a definition might include: Low density Discontiguous (“leapfrog”) development

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Alternative Measures of Urban Form in U.S. Metropolitan Areas

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Alternative Measures of Urban Form in U.S. Metropolitan Areas

Stephen Malpezzi

Wen-Kai Guo

University of Wisconsin-Madison

What is sprawl?

  • Most writers and activists fail to define sprawl. Some elements of a definition might include:

    • Low density

    • Discontiguous (“leapfrog”) development

    • Lack of public open space

  • Other outcomes that may or may not be associated with sprawl include:

    • High auto use, low transit use

    • Differences in the cost of public services

    • Excessive loss of farmland

Overall Plan for Malpezzi and Guo

  • Estimate a number of candidate measures of urban form

    • MSA specific indexes, based on Census tract data

  • Which incorporate the ‘most information’ about form?

    • Regress each index against other indexes, examine fit and t-statistics

  • Which are reasonably related to determinants?

    • Regress each index against a reasonable set of determinants

  • Link to second paper: take the best index, and run with it.

Candidate Indexes

  • Average MSA density

  • Sort tracts by their density. Pick density of tract containing the “median person.”

    • Many variations on this theme.

  • Estimate exponential density models

    • Univariate: intercept as well as delta, compare to flexible forms. Incorporate measures of fit.

  • Measures of dispersion

    • Gini, Theil indexes

  • Weighted average distances

    • to center; to all tracts

  • Gravity measures

  • Spatial autocorrelation

Selected Previous Research

  • A number of ‘sprawl’ papers examine average metropolitan density (Brueckner and Fansler, Peiser)

  • Many papers examine population density gradients, and related measures (Mills, Muth, etc., see McDonald review)

  • Compare and evaluate alternative measures

    • A fair number evaluate, e.g., power terms, test SUE model against a flexible alternative (e.g. Kau and Lee)

    • Only a few examine a fair range of alternatives (e.g. Song)

Sprawl, Related Issues

  • Bertaud and Malpezzi demonstrate that, in fact, cities like Paris and Los Angeles have much more efficient form than Seoul or Moscow, or Johannesburg.

  • What are the specific costs of sprawl which give rise to this concern? Are there benefits to “sprawl?” What are the most efficient policy responses?

    • E. Mills and B. Song, Urbanization and Urban Problems. Harvard, 1979.

    • G. Ingram, Land in Perspective. In Cullen and Woolrey, World Congress on Land Policy, DC Heath, 1982

    • A. Bertaud and S. Malpezzi, The Spatial Distribution of Population in 35 World Cities

Measuring Sprawl

  • Since sprawl is hard to define, it’s not surprising few papers have tried to measure it.

  • Many papers rely on average population density in the metro area.

  • Our usual density gradients

    • including power terms, R-squared

  • Moments of tract density

  • Gini coefficients, Theil information measures

  • Distance/gravity measures

  • Techniques of measuring spatial autocorrelation

  • Data reduction (principal components?)

Measuring Sprawl

  • Our initial measure will rely on tract densities within MSAs.

  • Sort each MSA’s census tracts by density, lowest to highest. Use the density of the tract containing the 10th percentile of MSA population, when tracts are so ordered.

    • Can use other percentiles (median, quartiles, etc.)

    • A better measure of density at the fringe.

    • Pros and cons?

  • Under development: average lot size for a “new” single family house, from AHS

Example of a measure based on order statistics: the average density of the tract containing the median of the MA population, when tracts are ranked by density.

Our MA has 7 tracts, total pop. is 100. Where is person 50?

The measure we focus on today.

  • The average density of the tract containing the 10th percentile of the metropolitan area’s population, when tracts are ranked by density. Say it 10 times, fast.

  • Pros:

    • Distinguishes between MAs with a lot of open space, and those without.

    • Gets at density on “the margin” without a particular assumption about monocentricity.

  • Cons:

    • There’s no guarantee that this “fringe” tract is really on the fringe.

    • The usual issues with using “gross” tract densities.

Costs and Benefits of Sprawl: The “Pure Cost” View


Costs per housing unit fall with density

Maximum feasible density, under

current rules and practices

Density of Development

Figure 1

Costs and Benefits of Sprawl: The Cost-Benefit View


Costs fall with density

Willingness-to-pay first rises, then

falls, with density

Maximum feasible density

Density of Development



Figure 2

Costs and Benefits of Sprawl: The Cost-Benefit View, with Externalities

Social costs (= private costs + external cost)


Private costs


Maximum feasible density

Density of Development







Figure 3

Figure 1-A

Figure 1-B

Figure 2

Figure 3

Figure 4

Figure 4

Figure 5

Figure 6

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14 (Preliminary)

Figure 15

Figure 16

Figure 6

Figure 7

Nine Causes of Sprawl (Richard K. Green)

  • Rent gradient

  • Demographics

  • Growing affluence

  • Transportation changes

  • Government service differentials

  • Racial discrimination and segregation

  • Plattage and plottage

  • Tax policy

  • Land use regulation

More causes of sprawl

  • Economic structure

  • The degree of monocentricity

  • Opportunity cost of land in rural uses

Some Opinions

  • American Farmland Trust, Farming on the Edge

  • Bank of America et al., Beyond Sprawl

  • Al Gore, several recent speeches

  • Peter Gordon and Harry Richardson, “Are Compact Cities a Desirable Planning Goal?”

  • Reid Ewing, “Is Los Angeles Style Sprawl Desirable?”

  • John Norquist, The Wealth of Cities

  • Richard Moe, Growing Smarter

  • Many more, type “sprawl” into your browser and stand back.

Some Literature

  • Real Estate Research Corporation, The Costs of Sprawl (1974)

  • Critiques of RERC by Altshuler (1977) and Windsor (1979)

  • Downs, New Visions for a Metropolitan America

  • Helen Ladd, “Population Growth, Density, and the Costs of Providing Public Services” (1992)

  • David Mills (1981)

  • Richard Peiser (1989)

  • Brueckner and Fansler (1983)

  • Burchell and Listokin, others at Rutgers, on “fiscal impact analysis” (various), The Costs of Sprawl Revisited (1998)

Highly Tentative Conclusions

  • Transit infrastructure has little effect on density per se.

  • More mass transit is associated with longer commutes.

  • Higher densities lower commutes, ceteris paribus.

  • Will these results hold up to further work?

Some Next Steps

  • Alternative sprawl measures (e.g. AHS new housing density)

  • Better measures of transit infrastructure

  • Model other outcomes that reflect potential costs and benefits of sprawl

    • environmental outcomes

    • public service costs

    • racial and economic segregation

  • Endogeneity, endogeneity, endogeneity

Percent of Metro Population and Employment in Central Cities

Source: O’Sullivan, Kain, Census

Why Do We Observe Decentralization?

  • Standard Urban Economics (SUE) model: rising incomes, falling transport costs

  • “Blight Flight” or Amenities/disamenities models

  • Public policies

  • Change in technology, shift to service economy, incubator processes?

The U.S. is Well-Endowed with Land

  • The U.S. has 7% of the world’s land area.

  • But 13% of the world’s cropland is in the U.S.

  • The U.S. has roughly 10 acres of land for every inhabitant.

Population Density, Selected Countries

U.S. Population if settled at other countries’ densities

How U.S. Urban Land is Used, 1980

Source: Vesterby and Heimlich, 1991

U.S. Land Use

  • Urban land is 3 percent of U.S. land by area, but the majority of land by value.

  • With about 4 hectares of land per person (gross), the U.S. is far from typical in density.

  • However, even very dense countries, like Korea, have small percentages of land in urban uses (see below).

U.S. Cropland and Urban Land Area

Figure A-2

USDA, Census

U.S. Cropland and Urban Land Area

  • While the share of U.S. land in urban uses has been growing (from a low base), cropland has been roughly constant over the last 40 years.

  • When relative prices warrant it, land can readily be converted from other uses to agriculture.

Some Big-Picture Land Use Questions (Indicative Only, Not Exhaustive)

  • Can we reconcile market approaches with social and ethical concerns?

    • Why have many economists focused so much on costs of regulation, not on benefits?

    • Why have many noneconomists neglected costs?

  • How can we get a better handle on the real social cost-benefit of different land uses?

    • Just because something’s hard to measure doesn’t mean it isn’t important

  • Can we focus more rigorously on distributional issues (as well as efficiency)?

More Land Use Questions

  • What’s the right system of incentives (taxes, subsidies, regulations, etc.)?

    • Lower order: for market participants?

    • Higher order: for planners and policymakers?

  • Urban decentralization (“sprawl”) is high on the public agenda. What can we say about costs and benefits, and appropriate responses?

  • Many other important land use issues, e.g.

    • Brownfields

    • Preservation

    • Central city/suburban/rural issues

Some General Things to Look for in a Cluster Hire in Land Use

  • Rigor

  • Open-mindedness

  • Some appreciation of the economics of land use (formal or informal)

  • Good institutional knowledge as well as technical training

  • Interest in urban and rural land use issues

  • Understanding related markets (e.g. transportation) would be a plus

Some objectives for a potential hire in land economics

  • Put the “sprawl” debate on a more rigorous footing: better definition and measurement, cost and benefits, determinants, policy recommendations

  • Enhance understanding of interactions among land use, general economic development, transport, real estate

  • What are the costs and benefits of different development patterns, of different public interventions?

  • How do land uses affect income distribution, racial and ethnic cleavages

  • Needs a strong economics background with demonstrated ability to work with noneconomists; knowledge of planning, law, institutions a plus

  • International as well as U.S. perspectives a plus

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